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Handbook of Damage Mechanics pp 1–49Cite as

Predicting Damage Evolution in Composites with Explicit Representation of Discrete Damage Modes

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Abstract

Polymer matrix composites (PMCs) are playing rapidly increasing roles in future military and civilian industries. Damage tolerance analysis is an integral part of PMC structural design. Considerable research efforts have been invested to establish predictive capabilities, but thus far high-fidelity strength and durability prediction capabilities are yet to be established. Advanced numerical methods that can explicitly resolve the multiple-damage processes and their nonlinear coupling at various scales are highly desired. This paper first reviews the recent development of advanced numerical methods, including eXtended Finite Element Method (X-FEM), phantom node methods (PNM), and the Augmented Finite Element Method (A-FEM), in handling the multiple-damage coupling in composites. The capability of these methods in representing various composite damage modes explicitly with embedded nonlinear fracture models (such as cohesive zone models) makes them excellent candidates for high-fidelity failure analyses of composites. The detailed formulation of A-FEM and its implementation to a popular commercial software package (ABAQUS) as a user-defined element has been given. Successful simulations of composites at various scales using the framework of A-FEM are presented and the numerical and material issues associated with these high-fidelity analyses are discussed. Through the numerical predictions and the direct comparisons to experimental results, it has been demonstrated that high-fidelity failure analyses can be achieved with the A-FEM through careful calibration of nonlinear material properties and cohesive fracture parameters and with proper considerations of the different length scales within which these damage processes operate.

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References

  • D.F. Adams, T.R. King, D.M. Blackketter, Evaluation of the transverse flexure test method for composite materials. Compos. Sci. Technol. 39, 341–353 (1990)

    Article  Google Scholar 

  • G. Bao et al., The role of material orthotropy in fracture specimens for composites. Int. J. Sol. Struct. 29, 1105–1116 (1992)

    Article  MATH  Google Scholar 

  • G.I. Barenblatt, The formation of equilibrium cracks during brittle fracture: general ideas and hypotheses, axially symmetric cracks. Appl. Math. Mech. 23, 622–636 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  • G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, in Advances in Applied Mechanics, ed. by H.L. Dryden, T. Von Karman (Academic, New York, 1962), pp. 55–129

    Google Scholar 

  • Z.P. Bazant, J. Planas, Fracture and Size Effect in Concrete and Other Quasibrittle Materials (CRC Press, Boca Raton, 1998)

    Google Scholar 

  • P.P. Camanho, C.G. Davila, M.F. De Moura, Numerical simulation of mixed-mode progressive delamination in composite materials. J. Compos. Mater. 37, 1415–1438 (2003)

    Article  Google Scholar 

  • P.P. Camanho et al., Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear. Compos. Part A Appl. Sci. Manuf. 37, 165–176 (2006)

    Article  Google Scholar 

  • A. Carpinteri, G. Colombo, Numerical analysis of catastrophic softening behaviour(snap-back instability). Comput. Struct. 31, 607–636 (1989)

    Article  Google Scholar 

  • A. Carpinteri, G. Ferro, Fracture assessment in concrete structures, in Concrete Structure Integrity, ed. by I. Milne, R.O. Ritchie, B. Karihaloo (Elsevier Science, Amsterdam, 2003)

    Google Scholar 

  • S.W. Case, K.L. Reifsnider, MRLife 12 Theory Manual – Composite Materials (Materials Response Group, Virginia Polytechnical Institute and State University, Blacksburg, 1999)

    Google Scholar 

  • J.L. Chaboche, P.M. Lesne, J.F. Maire, Continuum damage mechanics, anisotropy and damage deactivation for brittle materials like concrete and ceramic composites. Int. J. Damage Mech. 4(1), 5–22 (1995)

    Article  Google Scholar 

  • J.L. Chaboche, R. Girard, P. Levasseur, On the interface debonding models. Int. J. Damage Mech. 6, 220–256 (1997)

    Article  Google Scholar 

  • K.Y. Chang, S. Liu, F.K. Chang, Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings. J. Compos. Mater. 25, 274–301 (1991)

    Google Scholar 

  • H.Y. Choi, F.K. Chang, A model for predicting damage in graphite/epoxy laminated composites resulting from low-velocity point impact. J. Compos. Mater. 26, 2134–2169 (1992)

    Article  Google Scholar 

  • G. Clark, Modeling of impact damage in composite laminates. Composites 20, 209–214 (1989)

    Article  Google Scholar 

  • A. Corigliano, Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int. J. Sol. Struct. 30, 2779–2811 (1993)

    Article  MATH  Google Scholar 

  • B.N. Cox, Q.D. Yang, In quest of virtual tests for structural composites. Science 314, 1102–1107 (2006)

    Article  Google Scholar 

  • W.C. Cui, M.R. Wisnom, N. Jones, Failure mechanisms in three and four point short beam bending tests of unidirectional glass/epoxy. J. Strain. Anal. 27(4), 235–243 (1992)

    Article  Google Scholar 

  • C.G. Davila, P.P. Camanho, C.A. Rose, Failure criteria for FPR laminates. J. Compos. Mater. 39, 323–345 (2005)

    Article  Google Scholar 

  • R. de Borst, Numerical aspects of cohesive-zone models. Eng. Fract. Mech. 70, 1743–1757 (2003)

    Article  Google Scholar 

  • R. de Borst et al., On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials. Comput. Mech. 17(1–2), 130–141 (1995)

    Article  MATH  Google Scholar 

  • R. de Borst, J.J.C. Remmers, A. Needleman, Mesh-independent discrete numerical representations of cohesive-zone models. Eng. Fract. Mech. 73(2), 160–177 (2006)

    Article  Google Scholar 

  • J. Dowlbow, M. A. Kahaleel, J. Mitchell, Multiscale Mathematics Initiative: A Roadmap. A Report to Department of Energy Report PNNL-14966 (2004)

    Google Scholar 

  • D.S. Dugdale, Yielding of steel sheets containing slits. J. Mech. Phys. Sol. 8, 100–104 (1960)

    Article  Google Scholar 

  • G.J. Dvorak, N. Laws, Analysis of progressive matrix cracking in composite laminates. II. First ply failure. J. Compos. Mater. 21, 309–329 (1987)

    Article  Google Scholar 

  • M. Elices et al., The cohesive zone model: advantages, limitations and challenges. Eng. Fract. Mech. 69, 137–163 (2002)

    Article  Google Scholar 

  • X.J. Fang, Q.D. Yang, B.N. Cox, An augmented cohesive zone element for arbitrary crack coalescence and bifurcation in heterogeneous materials. Int. J. Numer. Meth. Eng. 88, 841–861 (2010)

    Article  MathSciNet  Google Scholar 

  • X.J. Fang et al., High-fidelity simulations of multiple fracture processes in a laminated composites in tension. J. Mech. Phys. Sol. 59, 1355–1373 (2011a)

    Article  MATH  Google Scholar 

  • X.J. Fang et al., An augmented cohesive zone element for arbitrary crack coalescence and bifurcation in heterogeneous materials. Int. J. Numer. Meth. Eng. 88, 841–861 (2011b)

    Article  MATH  Google Scholar 

  • A. Fawcett, J. Trostle, S. Ward, in International Conference on Composite Materials, Gold Coast, 1997

    Google Scholar 

  • S.F. Finn, Y.F. He, G.S. Springer, Delaminations in composite plates under transverse impact loads – experimental results. Compos. Struct. 23, 191–204 (1993)

    Article  Google Scholar 

  • J. Fish, A. Ghouali, Multiscale analysis sensitivity analysis for composite materials. Int. J. Numer. Meth. Eng. 50, 1501–1520 (2001)

    Article  MATH  Google Scholar 

  • C. Gonzalez, J. LLorca, Multiscale modeling of fracture in fiber-reinforced composites. Acta Mater. 54, 4171–4181 (2006)

    Article  Google Scholar 

  • S. Goutianos, B.F. Sorensen, Path dependence of truss-like mixed mode cohesive laws. Eng. Fract. Mech. 91, 117–132 (2012)

    Article  Google Scholar 

  • S. Hallett, M.R. Wisnom, Numerical investigation of progressive damage and the effect of layup in notched tensile tests. J. Compos. Mater. 40, 1229–1245 (2006a)

    Article  Google Scholar 

  • S.R. Hallett, M.R. Wisnom, Experimental investigation of progressive damage and the effect of layup in notched tensile tests. J. Compos. Mater. 40, 119–141 (2006b)

    Article  Google Scholar 

  • A. Hansbo, P. Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Meth. Appl. Mech. Eng. 193, 3523–3540 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • M.-Y. He, J.W. Hutchinson, Crack deflection at an interface between dissimilar materials. Int. J. Sol. Struct. 25, 1053–1067 (1989)

    Article  Google Scholar 

  • A. Hillerborg, M. Modéer, P.E. Peterson, Analysis of crack propagation and crack growth in concrete by means of fracture mechanics and finite elements. Cement. Concr. Res. 6, 773–782 (1976)

    Article  Google Scholar 

  • E.V. Iarve, D. Mollenhauer, R. Kim, Theoretical and experimental investigation of stress redistribution in open-hole composite laminates due to damage accumulation. Compos. Part A 36, 163–171 (2005)

    Article  Google Scholar 

  • H.M. Inglis et al., Cohesive modeling of dewetting in particulate composites: micromechanics vs. multiscale finite element analysis. Mech. Mater. 39, 580–595 (2007)

    Article  Google Scholar 

  • P.M. Jelf, N.A. Fleck, The failure of composite tubes due to combined compression and torsion. J. Mater. Sci. Lett. 29, 3080 (1994)

    Article  Google Scholar 

  • A.S. Kaddorur, M.J. Hinton, P.D. Soden, A comparison of the predictive capabilities of current failure theories for composite laminates: additional contributions. Compos. Sci. Technol. 64, 449–476 (2004)

    Article  Google Scholar 

  • M.S. Kafkalidis et al., Deformation and fracture of an adhesive layer constrained by plastically-deforming adherends. Int. J. Adhes. Sci. Technol. 14, 1593–1646 (2000)

    Article  Google Scholar 

  • M. Kumosa, G. Odegard, Comparison of the +/−45 tensile and Iosipescu shear tests for woven fabric composites. J. Compos. Technol. Res. 24, 3–15 (2002)

    Article  Google Scholar 

  • P. Ladeveze, Multiscale modelling and computational strategies. Int. J. Numer. Meth. Eng. 60, 233–253 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • I. Lapczyk, J. Hurtado, Progressive damage modeling in fiber-reinforced materials. Compos. Part A 38, 2333–2341 (2007)

    Article  Google Scholar 

  • F. Laurin, N. Carrere et al., A multi-scale progressive failure approach for composite laminates based on thermodynamical viscoelastic and damage models. Compos. Part A 38, 198–209 (2007)

    Article  Google Scholar 

  • D.S. Ling, Q.D. Yang, B.N. Cox, An augmented finite element method for modeling arbitrary discontinuities in composite materials. Int. J. Fract. 156, 53–73 (2009)

    Article  MATH  Google Scholar 

  • D.S. Ling et al., Nonlinear fracture analysis of delamination crack jumps in laminated composites. J. Aerosp. Eng. 24, 181–188 (2011)

    Article  Google Scholar 

  • J. LLorca, C. González, Multiscale modeling of composite materials: a roadmap towards virtual testing. Adv. Mater. 23, 5130–5147 (2011)

    Article  Google Scholar 

  • P. Maimi et al., A continuum damage model for composite laminates: Part I – Constitutive model. Mech. Mater. 39, 897–908 (2007)

    Article  Google Scholar 

  • A. Matzenmiller, J. Lubliner, R.L. Taylor, A constitutive model for anisotropic damage in fiber-composites. Mech. Mater. 20, 125–152 (1995)

    Article  Google Scholar 

  • L.N. McCartney, Physically based damage models for laminated composites. J. Mater. Des. Appl. 217(3), 163–199 (2003)

    Google Scholar 

  • J. Mergheim, E. Kuhl, P. Steinmann, A finite element method for the computational modeling of cohesive cracks. Int. J. Numer. Meth. Eng. 63, 276–289 (2005)

    Article  MATH  Google Scholar 

  • N. Moës, T. Belytschko, Extended finite element method for cohesive crack growth. Eng. Fract. Mech. 69, 813–833 (2002)

    Article  Google Scholar 

  • N. Moes, J. Dolbow, T. Belytschko, Finite element method for crack growth without remeshing. Int. J. Numer. Meth. Eng. 46, 131–150 (1999)

    Article  MATH  Google Scholar 

  • A. Needleman, An analysis of decohesion along an imperfect interface. Int. J. Fract. 42, 21–40 (1990)

    Article  Google Scholar 

  • T.K. O’Brien, S.A. Salpekar, Scale effects on the transverse tensile strength of carbon/epoxy composites. Compos. Mater. Test. Des. 11(ASTM STP 1206), 23–52 (1993)

    Google Scholar 

  • T.K. O'Brien et al., Influence of specimen configuration and size on composite transverse tensile strength and scatter measured through flexure testing. J. Compos. Technol. Res. 25, 50–68 (2003)

    Google Scholar 

  • J.T. Oden, K. Vemaganti, N. Moes, Hierarchical modeling of heterogeneous solids. Comput. Method. Appl. Mech. Eng. 172, 3–25 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • J.T. Oden et al., Simulation-Based Engineering Science – Revolutionizing Engineering Science through Simulation (NSF, 2006)

    Google Scholar 

  • C. Oskay, J. Fish, Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput. Methods Appl. Mech. Eng. 196, 1216–1243 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • J. Parmigiani, M.D. Thouless, The roles of toughness and cohesive strength on crack deflection at interfaces. J. Mech. Phys. Sol. 54, 266–287 (2006)

    Article  MATH  Google Scholar 

  • J. Parmigiani, M.D. Thouless, The effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries. Eng. Fract. Mech. 74, 2675–2699 (2007)

    Article  Google Scholar 

  • S.T. Pinho, P. Robinson, L. Iannucci, Fracture toughness of the tensile and compressive fibre failure modes in laminated composites. Compos. Sci. Technol. 66, 2069–2079 (2006)

    Article  Google Scholar 

  • S. Ramanathan, D. Ertaz, D.S. Fisher, Quasistatic crack propagation in heterogeneous media. Phys. Rev. Lett. 79, 873–876 (1997)

    Article  Google Scholar 

  • J.N. Reddy, Multiscale computational model for predicting damage evolution in viscoelastic composites subjected to impact loading technical report to U.S. Army Research Office, 1-31 (2005)

    Google Scholar 

  • J.J.C. Remmers, R. de Borst, A. Needleman, A cohesive segments method for the simulation of crack growth. Comput. Mech. 31(1–2), 69–77 (2003)

    Article  MATH  Google Scholar 

  • S. Rudraraju et al., In-plane fracture of laminated fiber reinforced composites with varying fracture resistance: experimental observations and numerical crack propagation simulations. Int. J. Sol. Struct. 47, 901–911 (2010)

    Article  MATH  Google Scholar 

  • S. Rudraraju et al., Experimental observations and numerical simulations of curved crack propagation in laminated fiber composites. Compos. Sci. Technol. 72, 1064–1074 (2011)

    Article  Google Scholar 

  • K.W. Shahwan, A.M. Waas, Non-self-similar decohesion along a finite interface of unilaterally constrained delaminations. Proc. Roy. Soc. Lon. A 453, 515–550 (1997)

    Article  MathSciNet  Google Scholar 

  • M.M. Shokrieh, L.B. Lessard, Progressive fatigue damage modeling of composite materials, Part I: Modeling. J. Compos. Mater. 34(13), 1056–1080 (2000)

    Article  Google Scholar 

  • S.J. Song, A.M. Waas, Energy-based mechanical model for mixed mode failure of laminated composites. AIAA J. 33, 739–745 (1995)

    Article  Google Scholar 

  • J.H. Song, P.M.A. Areias, T. Belytschko, A method for dynamic crack and shear band propagation with phantom nodes. Int. J. Numer. Meth. Eng. 67, 868–893 (2006)

    Article  MATH  Google Scholar 

  • R. Talreja, Multiscale modeling in damage mechanics of composite materials. J. Mater. Sci. 41, 6800–6812 (2006)

    Article  Google Scholar 

  • X.D. Tang et al., Progressive failure analysis of 2x2 braided composites exhibiting multiscale heterogeneity. Compos. Sci. Technol. 66, 2580–2590 (2006)

    Article  Google Scholar 

  • T.-E. Tay, Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001. Appl. Mech. Rev. 56(1), 1–32 (2003)

    Article  Google Scholar 

  • M.D. Thouless, Crack spacing in brittle films on elastic substrates. J. Am. Ceram. Soc. 73, 2144–2146 (1990)

    Article  Google Scholar 

  • M.D. Thouless, Q.D. Yang, A parametric study of the peel test. Int. J. Adhes. Adhes. 28, 176–184 (2008)

    Article  Google Scholar 

  • A. Turon et al., A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mech. Mater. 38, 1072–1089 (2006)

    Article  Google Scholar 

  • A. Turon et al., An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng. Fract. Mech. 74, 1665–1682 (2007)

    Article  Google Scholar 

  • F.P. Van de Meer, L.J. Sluys, Continuum models for the analysis of progressive failure in composite laminates. J. Compos. Mater. 43, 2131–2156 (2009a)

    Article  Google Scholar 

  • F.P. Van de Meer, L.J. Sluys, A phantom node formulation with mixed mode cohesive law for splitting in laminates. Int. J. Fract. 158, 107–124 (2009b)

    Article  MATH  Google Scholar 

  • F.P. Van de Meer, C. Oliver, L.J. Sluys, Computational analysis of progressive failure in a notched laminate including shear nonlinearity and fiber failure. Compos. Sci. Technol. 70, 692–700 (2010)

    Article  Google Scholar 

  • A.S.D. Wang, F.W. Crossman, Initiation and growth of transverse cracks and delaminations. J. Compos. Mater. 14, 71–87 (1980)

    Article  Google Scholar 

  • J.S. Wang, Z. Suo, Experimental determination of interfacial toughness using Brazil-nut-sandwich. Acta Metall. 38, 1279–1290 (1990)

    Article  Google Scholar 

  • M.R. Wisnom, The effect of fibre rotation in +/−45 degree tension tests on measured shear properties. Composites 26, 25–32 (1994)

    Article  Google Scholar 

  • M.R. Wisnom, F.-K. Chang, Modelling of splitting and delamination in notched cross-ply laminates. Compos. Sci. Technol. 60, 2849–2856 (2000)

    Article  Google Scholar 

  • M.R. Wisnom, M.I. Jones, Size effects in interlaminar tensile and shear strength of unidirectional glass fibre/epoxy. J. Reinf. Plast. Compos. 15, 2–15 (1996)

    Google Scholar 

  • D. Xie et al., Discrete cohesive zone model to simulate static fracture in 2D tri-axially braided carbon fiber composites. J. Compos. Mater. 40, 2025–2046 (2006)

    Article  Google Scholar 

  • Q.D. Yang, B.N. Cox, Cohesive zone models for damage evolution in laminated composites. Int. J. Fract. 133(2), 107–137 (2005)

    Article  MATH  Google Scholar 

  • Q.D. Yang, M.D. Thouless, Mixed mode fracture of plastically-deforming adhesive joints. Int. J. Fract. 110, 175–187 (2001a)

    Article  Google Scholar 

  • Q. Yang, M.D. Thouless, Mixed mode fracture of plastically-deforming adhesive joints. Int. Fract. 110, 175–187 (2001b)

    Article  Google Scholar 

  • Q.D. Yang, M.D. Thouless, S.M. Ward, Numerical simulations of adhesively-bonded beams failing with extensive plastic deformation. J. Mech. Phys. Sol. 47, 1337–1353 (1999)

    Article  MATH  Google Scholar 

  • Q.D. Yang, M.D. Thouless, S.M. Ward, Elastic–plastic mode-II fracture of adhesive joints. Int. J. Sol. Struct. 38, 3251–3262 (2001)

    Article  MATH  Google Scholar 

  • Q.D. Yang et al., Fracture and length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials 27, 2095–2113 (2006a)

    Article  Google Scholar 

  • Q.D. Yang et al., Re-evaluating the toughness of human cortical bone. Bone 38, 878–887 (2006b)

    Article  Google Scholar 

  • Q.D. Yang et al., An improved cohesive element for shell delamination analyses. Int. J. Numer. Meth. Eng. 83(5), 611–641 (2010)

    MATH  Google Scholar 

  • Q.D. Yang et al., Virtual testing for advanced aerospace composites: advances and future needs. J. Eng. Mater. Technol. 133, 11002–11008 (2011)

    Article  Google Scholar 

  • Q.D. Yang, X. J. Fang, Revisiting crack kinking in cohesive materials. Unpublished results, 2013

    Google Scholar 

  • T. Ye, Z. Suo, A.G. Evans, Thin film cracking and the roles of substrate and interface. Int. J. Sol. Struct. 29, 2639–2648 (1992)

    Article  Google Scholar 

  • Z. Zhang, Z. Suo, Split singularities and the competition between crack penetration and debond at a bimaterial interface. Int. J. Struct. 44, 4559–4573 (2007)

    Article  MATH  Google Scholar 

  • Z.Q. Zhou et al., The evolution of a transverse intra-ply crack coupled to delamination cracks. Int. J. Fract. 165, 77–92 (2010)

    Article  Google Scholar 

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  1. Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL, 33124, USA

    Dr. Q. D. Yang & B. C. Do

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  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, Louisiana, USA

    George Z. Voyiadjis

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Yang, Q.D., Do, B.C. (2014). Predicting Damage Evolution in Composites with Explicit Representation of Discrete Damage Modes. In: Voyiadjis, G. (eds) Handbook of Damage Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8968-9_16-1

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